The Erlang loss function, which gives the steady state loss probability in an M/M/s/s system, has been extensively studied in the literature. The paper looks at the similar loss probability in M/M/s/s+c systems and an extension of it to nonintegral number of servers and queue capacity. It studies its monotonicity properties. The paper shows that the loss probability is convex in the queue capacity, and that it is convex in the traffic intensity ρ if ρ is below some ρ* and concave if ρ is greater than ρ*, for a broad range of number of servers and queue capacities. It proves that the one-server loss system is the only M/M/s/s+c system for which the loss probability is concave in the traffic intensity in all its range.
